In electrical generators the aim is always to maximize the magnetic flux threading the coils in which the generated current flows because the electromotive force generated is directly proportional to that flux. Three factors determine total flux: (1) flux density, (2) threaded coil area, and (3) number of coils. An extremely useful magnetic generator is described in the inventor's U.S. patent application Ser. No. 09/034,073, entitled "Cylindrical Permanent Magnet Magic Ping Electric Motor and Generator," which is incorporated herein by reference. That application describes a generator in which a rotating magic cylinder provides a high magnetic field that threads a compact coil in its central cavity causing a large flux through the coil. In that device, the cylinder's rotation causes the flux to alternate because, the angle of the field with respect to the plane of the coil changes linearly with time, and the area of the coil normal to the field varies periodically based on the formula: EQU A.sub.n =A sin .omega.t (1)
where A is coil area and A.sub.n is the area of the coil normal to the field. Based on this relationship, the total flux can vary sinusoidally because magnetic flux: EQU .PHI.=HA.sub.k =H A sin .omega.t=.PHI..sub.A sin .omega.t (2)
where .PHI..sub.A is flux amplitude. Since the induced electromotive force is proportional to the flux, the electromotive force is also sinusoidal, resulting in an Alternating Current. The field magnitude in that device's coil material is constant (H) and induces lossy eddy currents that are proportional to the square of the field magnitude.
The present invention provides a pair of coaxial nested magnetic cylinders rotated with respect to each other so that each cylinder contributes the same amount of magnetic field to the total, i.e. each contributes H/2. In order to accomplish this, it is necessary for the radius, r.sub.b, of the border between the inner and outer cylinders, be calculated according to the following formula: EQU r.sub.b =r.sub.i +L r.sub.o (3)
where r.sub.i is the radius of the core cavity and r.sub.o is the outer radius of the system. The devices of the present invention generate currents equivalent to the single rotating magnetic cylinder, without the disadvantages, shortcomings and limitations of eddy current losses experienced by single rotating magnetic cylinders.